Cut chicken into 1-inch (2.5 cm) cubes. In large bowl, toss together chicken, lemon rind and juice, oil, oregano, salt and pepper; let stand for 10 minutes to marinate.
Alternately thread chicken and onion onto 4 metal skewers. Broil on foil-lined rimmed baking sheet, turning once, until chicken is no longer pink inside, about 10 minutes.
Meanwhile, cut cucumber in half lengthwise; thinly slice crosswise to make 1 cup (250 mL).
Spread tzatziki over half of each pita. Push chicken and onion off skewers onto pitas. Top with tomato, cucumber and lettuce; fold over.